Multiplicities and tensor product coefficients for $A_r
We apply some recent developments of Baldoni-DeLoera-Vergne on vector partition functions, to Kostant and Steinberg formulas, in the case of $A_r$. We therefore get a fast {\sc Maple} program that computes for $A_r$: the multiplicity $c_{\lambda,\mu}$ of the weight $\mu$ in the representation $V(\la...
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Main Author | |
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Format | Journal Article |
Language | English |
Published |
20.06.2003
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Subjects | |
Online Access | Get full text |
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Summary: | We apply some recent developments of Baldoni-DeLoera-Vergne on vector
partition functions, to Kostant and Steinberg formulas, in the case of $A_r$.
We therefore get a fast {\sc Maple} program that computes for $A_r$: the
multiplicity $c_{\lambda,\mu}$ of the weight $\mu$ in the representation
$V(\lambda)$ of highest weight $\lambda$; the multiplicity
$c_{\lambda,\mu,\nu}$ of the representation $V(\nu)$ in $V(\lambda)\otimes
V(\mu)$. The computation also gives the locally polynomial functions
$c_{\lambda,\mu}$ and $c_{\lambda,\mu,\nu}$. |
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DOI: | 10.48550/arxiv.math/0306308 |